Gas Collisions in Containers: Comparing Ratios of Wall Collisions"

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SUMMARY

The discussion centers on calculating the ratio of gas wall collisions in two containers with differing temperatures. The gas in the first container has a Kelvin temperature four times that of the second container. Using the equation for root mean square speed (Urms = sqrt(3.R.T/M)) and the relationship between collisions and Urms, the ratio of collisions can be determined. The correct answer is B) 4:1, as the number of collisions is proportional to the temperature of the gas.

PREREQUISITES
  • Understanding of the Ideal Gas Law (PV=nRT)
  • Knowledge of root mean square speed (Urms = sqrt(3.R.T/M))
  • Familiarity with kinetic energy equations (Kinetic energy average = 3/2 RT)
  • Basic concepts of molecular mass and particle density
NEXT STEPS
  • Study the derivation of the Ideal Gas Law and its applications
  • Learn about the implications of temperature on gas behavior and collision frequency
  • Explore the relationship between kinetic energy and temperature in gases
  • Investigate advanced topics in statistical mechanics related to gas collisions
USEFUL FOR

Students in physics or chemistry courses, educators teaching gas laws, and anyone interested in thermodynamics and molecular behavior of gases.

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Homework Statement


You have two samples of the same gas in the same size container, with the same pressure. The gas in the first container has a kelvin temperature four times that of the gas in the other container.

The ratio of number of collisions with the wall in the first container compared to that in the second is:
A) 1:1
B) 4:1
C) 1:4
D) 2:1
E) 1:2

Homework Equations


PV=nRT
Urms = sqrt(3.R.T/M)
collisions= m.Urms^2
Kinetic energy average= 3/2 RT

The Attempt at a Solution


I find that n2 = 4n1
but what I should do after that?
I tried relating the kinetic energy but it didn't work with me.
How we can approach to such problems? What rules should we use
 
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Any Help said:

Homework Statement


You have two samples of the same gas in the same size container, with the same pressure. The gas in the first container has a kelvin temperature four times that of the gas in the other container.

The ratio of number of collisions with the wall in the first container compared to that in the second is:
A) 1:1
B) 4:1
C) 1:4
D) 2:1
E) 1:2

Homework Equations


PV=nRT
Urms = sqrt(3.R.T/M)
collisions= m.Urms^2
Kinetic energy average= 3/2 RT

The Attempt at a Solution


I find that n2 = 4n1
but what I should do after that?
I tried relating the kinetic energy but it didn't work with me.
How we can approach to such problems? What rules should we use

It is a bit difficult to help since you don't define the meaning of any variables. Some of them are maybe obvious. But, what is ##m## and ##M##?
if ##m## is the mass/particle and ##M## is the total you would have ##M/m=n##. However, I would start by putting the expressions for ##U_{\mathrm{rms}}## in the expression for "collisions", leading to an expression for "collisions" depending on ##m/M##.
 

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